E. H. Abdalaoui, On the pointwise convergence of multiple ergodic averages, arXiv:1406

E. H. El-abdalaoui, J. Kulaga-przymus, M. Lemanczyk, and &. T. De-la-rue, The Chowla and the Sarnak conjectures from ergodic theory point of view, Discrete Contin, Dyn. Syst, vol.37, issue.6, pp.2899-2944, 2017.

I. Assani, Multiple recurrence and almost sure convergence for weakly mixing dynamical systems, Israel Journal of Mathematics, vol.17, issue.1, pp.111-124, 1998.
DOI : 10.1007/BF02762270

I. Assani, D. Duncan, and R. Moore, Pointwise characteristic factors for Wiener-Wintner double recurrence theorem, Erg. Th. and Dyn. Sys, pp.1037-1066

I. Assani and R. Moore, Extension of Wiener-Wintner double recurrence theorem to polynomials

J. Bourgain, Double recurrence and almost sure convergence, J. Reine Angew. Math, vol.404, pp.140-161, 1990.

J. Bourgain, P. Sarnak, and T. Ziegler, Disjointness of Moebius from horocycle flows, From Fourier analysis and number theory to Radon transforms and geometry, Dev. Math, vol.28, pp.67-83, 2013.

Q. Chu, Convergence of weighted polynomial multiple ergodic averages, Proceedings of the American Mathematical Society, vol.137, issue.04, pp.1363-1369, 2009.
DOI : 10.1090/S0002-9939-08-09614-7
URL : https://hal.archives-ouvertes.fr/hal-00257899

H. Davenport, On some infinite series involving arithmetical functions, II, Quart. J. Math. Oxf, vol.8, pp.313-320, 1937.

C. Demeter, Pointwise convergence of the ergodic bilinear Hilbert transform, Illinois J.Math, vol.514, pp.1123-1158, 2007.

C. Demeter, T. Tao, and C. Thiele, Maximal multilinear operators, Transactions of the American Mathematical Society, vol.360, issue.09, pp.4989-5042, 2008.
DOI : 10.1090/S0002-9947-08-04474-7
URL : http://arxiv.org/abs/math/0510581

N. Etemadi, An elementary proof of the strong law of large numbers, Zeitschrift f?r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.1, issue.1, pp.119-122, 1981.
DOI : 10.1007/BF01013465

H. Furstenberg, Recurrence in ergodic theory and combinatorial number theory, M. B. Porter Lectures, 1981.

A. Garcia, Topics in almost everywhere convergence, 1970.

B. Green and T. Tao, The M?bius function is strongly orthogonal to nilsequences, Annals of Mathematics, vol.175, issue.2, pp.541-566, 2012.
DOI : 10.4007/annals.2012.175.2.3

Y. Gutman, W. Huang, S. Shao, and X. Ye, Almost sure convergence of the multiple ergodic average for certain weakly mixing systems

L. K. Hua, Additive theory of prime numbers, Translations of Mathematical Monographs, vol.13, 1965.

B. Host, Mixing of all orders and pairwise independent joinings of systems with singular spectrum, Israel Journal of Mathematics, vol.13, issue.3, pp.289-298, 1991.
DOI : 10.1007/BF02773866

W. Huang, S. Shao, and X. Ye, Pointwise convergence of multiple ergodic averages and strictly ergodic models

. Rudin, Walter Fourier analysis on groups. Reprint of the 1962 original, 1990.
DOI : 10.1002/9781118165621
URL : https://babel.hathitrust.org/cgi/imgsrv/download/pdf?id=mdp.39015000491434;orient=0;size=100;seq=7;attachment=0

P. Sarnak, Möbius randomness and dynamics, Not. S. Afr. Math. Soc, vol.43, issue.2, pp.89-97, 2012.

E. M. Stein and R. Shakarchi, Fourier analysis, An introduction, Princeton Lectures in Analysis, 2003.

E. C. Titchmarsh, The theory of the Riemann zeta-function, Second edition, 1986.

J. Thouvenot, La convergence presque sûre des moyennes ergodiques suivant certaines soussuites d'entiers (d'après Jean Bourgain) (French) [Almost sure convergence of ergodic means along some subsequences of integers (after Jean Bourgain)] Séminaire Bourbaki, pp.189-190, 1989.

T. Zhan, Davenport's theorem in short intervals, Chin. Ann. of Math, vol.12, issue.4, pp.421-431, 1991.

P. Zorin-kranich, A nilsequence wiener wintner theorem for bilinear ergodic averages